On windy days, the edges of a skyscraper cause a lot of turbulence in the air.
Wind curls around in swirling vortex formations, much like water swirling around a rock in a stream. Each vortex formation is unstable. Every minute or so a new one pulls away from the building, first off one side, then the other, to fly away downwind. Each shedding vortex tugs the building sideways, causing it to vibrate slightly.
For well designed buildings, this isn't a problem. It's only a slight tug, first one way, then the other. However, every object has a natural frequency that it especially likes to vibrate at.
Swing Set Vs. Skyscraper
Consider a child on a swing set. The slow back and forth rhythm is the swing's natural frequency. If you follow that rhythm, and give your child a slight push every time she swings back to you, you can make her swing higher and higher. All your little pushes add up to a lot of motion. If you ignore the swing's natural frequency and just start pushing randomly, your child won't swing very well.
If a building is poorly designed, the gentle back and forth tug of vortex shedding might happen at the building's exact natural frequency. Like a child on a swing, the building can begin swaying wildly, each small tug adding to the total motion.
Engineers design skyscrapers to behave like the second example, a swing that's pushed randomly. They figure out how vortex shedding will tug at the building, and make sure the natural frequency is nowhere near that rate. While this wouldn't be much fun on a swing set, it's certainly reassuring up on the hundredth floor.